Slope-matched stylus tool for incremental sheet forming

ABSTRACT

A slope-matched stylus (SMS) tool for Incremental Sheet Forming (ISF) of a sheet includes a shaft connected to a stylus body and to a multi-axis drive mechanism. The stylus body has a conical or generally frustoconical form which includes a tool surface defining one or more corresponding tool wall angles. The tool wall angle range matches one or more part wall angles of a part formed via the ISF process, such that a flat line of contact exists between the stylus body and sheet. The tool and part wall angles are complementary. A system includes the tool and drive mechanism. A method includes securing the sheet to a fixture, connecting the tool to the drive mechanism, and progressively pressing a tool surface of the stylus body into or against the sheet using the drive mechanism, controlling the latter to ensure a flat line of contact is provided between the stylus body and sheet.

BACKGROUND

Sheet metal fabrication involves the targeted deformation of a fixtured sheet metal blank for the purpose of shaping the captive blank into a finished part having a desired three-dimensional (3D) surface geometry. Of the myriad of available sheet metal fabrication techniques, Incremental Sheet Forming (ISF) in particular involves the progressive incremental elastoplastic deformation of the blank using a stylus tool. The stylus tool, which is typically hemispherical in shape, is position-controlled by a 3-axis computer numeric control (CNC) machine as the blank remains securely clamped within a frame in a nominal Cartesian xy-plane, with the frame possibly being moveable. Partial or full perimeter securing of the blank may include constraining the movement of all or only part of the perimeter of the blank with respect to the frame.

ISF is highly agile relative to competing sheet metal fabrication processes such as deep drawing, during which a sheet metal blank is drawn into a forming die by operation of a punch. For instance, ISF enables the formation of 3D parts without resorting to expensive steel tooling, such as dies and/or punches, the constructions of which are typically specific to the geometry of the particular part being formed. Some ISF variants such as Single Point Incremental Forming (SPIF) and Dual Sided Incremental Forming (DSIF) do not require dies, whilst other variants such as Two Point Incremental Forming (TPIF) can utilize lower cost tooling materials such as plastic or wood to construct male or female backing dies.

The lead times and costs typically associated with tooling production and implementation using alternative/non-steel materials are generally much lower than the lead times and costs of using the steel materials of deep drawing tooling. For instance, lower cost alternative materials can be used during ISF due, e.g., to the difference in loading that the die tool typically experiences during the forming process. That is, because of the small area of contact between the stylus tool and the sheet material, the total load imposed on the die at any given time during ISF is only a fraction of that seen in competing techniques such as deep drawing or hydroforming. Although progressive motion control and incremental stepdown sequencing renders ISF processes slower than higher volume approaches such as deep drawing, ISF nevertheless remains a viable alternative process, such as when manufacturing low-volume, custom, or out-of-production parts across a wide range of industries.

SUMMARY

Disclosed herein are slope-matched stylus (SMS) tools and related systems and methods for performing an Incremental Sheet Forming (ISF) process. The disclosed solutions rely on a specially shaped stylus body to reduce elastic springback and surface waviness of three-dimensional (3D) parts having shallow wall angles, with the realized springback and surface waviness reduction being relative to results typically achieved using traditional ISF techniques. In this manner, the present teachings extend the benefits of ISF processes to the formation of a much wider variety of 3D parts.

As appreciated in the art, a conventional cylindrical stylus tool having a hemispherical or blunted working surface, and controlled via an associated 3-axis computer numeric control (CNC) machine, is not ideally suited to the formation of relatively shallow/low-profile parts, particularly those having very mild surface curvatures. As a result, such stylus tools are suboptimal when forming 3D parts having shallow part wall angles, with “shallow” as used herein generally referring to part wall angles of less than about 20° relative to horizontal, and possibly as shallow as just a few degrees. Stylus tools used during an ISF process impart tensile strain in a direction that is perpendicular to the tool's direction of travel, with the amount of tensile strain generally varying through the sheet thickness. In response to the gradient of tensile strain through the sheet thickness, the captive sheet tends to curl in a direction perpendicular to the stylus tool's direction of travel. The undesirable curling behavior can become particularly problematic when forming sheets into shallow 3D shapes, as very little out-of-plane stiffness is present for the purpose of reacting to the undesirable curling behavior.

Furthermore, for ISF formed parts having a shallow part wall angle and mild surface curvature, accumulation of curling in the sheet during forming results in significant elastic “springback”, i.e., the resilient return response exhibited by the 3D part as the clamping force is relieved. Moreover, z-level toolpaths are commonly spaced apart in comparison to the width of stylus tool engagement, which in turn can result in undesirable surface waviness in the formed part. While the particular problem of surface waviness can be minimized to some extent by reducing the z-axis step-down (Δz) such reduction further exacerbates the springback problem. The present solutions are therefore intended to mitigate elastic springback, surface waviness, curling, and other possible quality issues such as stepdown-related surface divots or markings as set forth below.

To this end, the SMS tool having a surface geometry constructed as described herein may be used in an ISF process during which a 3D part, e.g., an out-of-production aircraft replacement component, is progressively fabricated from a planar material blank (“sheet”). For illustrative consistency, the sheet is described below as being a sheet metal blank, such as an aerospace grade aluminum or alloy. However, application-suitable non-metallic or composite materials may possibly be used in other embodiments. Thus, sheet metal is just one possible material composition of the contemplated sheet.

The SMS tool according to an exemplary embodiment includes a shaft, e.g., an elongated cylindrical rod or shank, with the shaft having a longitudinal axis and opposing distal ends. A first distal end of the shaft is configured to connect to a multi-axis drive mechanism, e.g., a 3-axis, 4-axis, or 5-axis CNC machine or possibly a multi-axis robot in different embodiments and representative use cases. The SMS tool includes a stylus body connected to a second distal end of the shaft. Unlike conventional hemispherical stylus tools, the stylus body disclosed herein has at least one tool surface defining a corresponding slope, herenafter a “tool wall angle”, relative to a longitudinal axis of the shaft. The corresponding tool angle “matches” a part wall angle of the part, with the terms “matches” and “matching” as contemplated herein meaning the part wall angles and tool wall angles are geometrically complementary angles, i.e., summing to 90°

$\left( {\frac{\pi}{2}{radians}} \right)$

along a line of contact present between the stylus body and an exposed working surface of the sheet.

A stylus body of the SMS tool in a general configuration is described by the frustum of a cone. The cone has an abritrary covex cross section and may be slanted. The two planes which define the frustum form the top (base) and bottom (tip) surfaces of the stylus body. In the simplest embodiment, the noted cone is a right angled cone having a circular cross section. The bottom tool plane and the apex plane are coincident, and the apex of the cone is filleted to produce a rounded tip surface. A sloped sidewall of a constant tool wall angle extends from a planar base surface of the stylus body, located within the top tool plane as described herein, and terminates at the rounded tip surface. The base surface is connected to or formed integrally with the second distal end of the shaft. The corresponding tool wall angle may be a single tool angle in a representative embodiment, e.g., less than about 20° relative to horizonal or as shallow as about 5° in different non-limiting exemplary embodiments.

In other embodiments, the cross section of the cone is non-circular and the cone may be slanted. Such a configuration allows the stylus body to be constructed with multiple different corresponding tool wall angles, with a sweep angle range defined between angular limits, i.e., relatively steep and relatively shallow tool wall angles. Representative embodiments of the tool wall angles include a relatively shallow tool wall angle of, e.g., about 5° to about 20° as noted above. A relatively steep tool wall angle of about 55° to about 70° is also possible, as set forth herein, up to about 90° in some configurations.

The stylus tool may be used to form a 3D part having part wall angles varying anywhere within the defined sweep angle range. In operation, a particular part wall angle of the 3D part is matched to the presented tool wall angle by operation of the multi-axis drive mechanism, i.e., by rotating the SMS tool until an attitude or angular orientation of the stylus body results in geometrically complementary slopes. In other words, rotations occurs until the presented tool wall angle of the stylus body geometrically complements the slope of the particular presented surface of the 3D part being formed.

The tool surface (working surface) of the stylus body may be arranged orthogonal/normal to the longitudinal axis of the shaft in another aspect of the disclosure. The multi-axis drive mechanism in this instance may be embodied as a 5-axis drive mechanism, with the tool surface of the stylus body being pressed into or against the sheet by the 5-axis drive mechanism to align the longditudinal axis of the tool shaft approximately normal to the surface of the 3D part along the line, or at a plane, of contact. Thus, the tool surface remains aligned to a local tangent plane of the 3D part being formed, i.e., a centerline of the tool remains colinear with the surface normal.

Also disclosed herein is a related system for use in an ISF process during which a 3D part is progressively fabricated from a sheet, e.g., a sheet metal blank as noted above. The system according to a non-limiting embodiment includes the multi-axis drive mechanism and the SMS tool. As summarized above, the shaft includes a longitudinal axis, a first distal end connected to the multi-axis drive mechanism, and a second distal end connected to the stylus body. Depending on the configuration, the stylus body may include at least one working surface defining a corresponding tool wall angle. The tool wall angle in turn complements a part wall angle of the 3D part as noted above, such that a flat line of contact is provided between the stylus body and the sheet during the ISF process.

In another aspect of the subject disclosure, an ISF method is disclosed during which a 3D part is progressively fabricated from the above-described sheet. The method in a representative embodiment includes securing the sheet to a fixture, as well as connecting a first distal end of the above-noted shaft of the SMS tool to the multi-axis drive mechanism. As summarized above, the SMS tool has a stylus body that is connected to a second distal end of the shaft, with the SMS tool being axisymmetric or non-axisymmetric in different configurations.

The method as described herein includes progressively pressing or forcing a tool surface of the stylus body into or against the sheet via the multi-axis drive mechanism when forming the 3D part. The tool surface in the various embodiments of the exemplary method defines one or more tool wall angles relative to the longitudinal axis of the shaft, each tool wall angle matching a corresponding part wall angle of the 3D part being formed. This structure ensures that throughout the ISF process, a flat line of contact is provided between the stylus body and the sheet, with the above-noted complementary tool and part wall angles defined along the flat line of contact.

The above summary is not intended to represent every possible embodiment or every aspect of the present disclosure. Rather, the foregoing summary is intended to exemplify some of the novel aspects and features disclosed herein. The above features and advantages, and other features and advantages of the present disclosure, will be readily apparent from the following detailed description of representative embodiments and modes for carrying out the present disclosure when taken in connection with the accompanying drawings and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A schematically illustrates a representative incremental sheet forming (ISF) process utilizing a slope-matched stylus (SMS) tool configured in accordance with the present disclosure.

FIGS. 1B, 1C, and 1D are partial cutaway perspective view illustrations of different representative ISF processes using SMS tools in accordance with the present disclosure.

FIGS. 2A and FIG. 2B are schematic geometric illustrations of a frustoconical shape of the SMS tool according to an embodiment.

FIG. 2C is a schematic geometric illustration showing the relationship between the tool wall angle and a cross section defined on the top tool plane as described herein.

FIG. 3 is an illustration of an axisymmetric SMS tool having a single slope or tool wall angle according to a possible embodiment.

FIG. 4A is a cross section of an SMS tool configured with multiple slopes or tool wall angles for which there is one plane of symmetry.

FIG. 4B is a plan view illustration of the SMS tool shown in FIG. 4A.

FIG. 4C is a plan view illustration of SMS tool shown in FIG. 4A showing the sweep angle, clocking angle, and related items.

FIGS. 4D and 4E are perspective view illustrations of the SMS tool of FIG. 4A.

FIG. 5A is a plan view illustration of an SMS tool configured with multiple slopes or tool wall angles for which there is no symmetry.

FIG. 5B is a side view illustration of the SMS tool shown in FIG. 5A.

FIGS. 5C and 5D are perspective view illustrations of the SMS tool of FIG. 5A.

FIG. 6 is a perspective illustration of the SMS tool according to yet another embodiment.

FIG. 7 is a perspective illustration showing an advantage of using an SMS tool on a shallow walled part.

FIG. 8 is a flow chart describing an SMS method according to a representative embodiment.

FIGS. 9A and 9B are plan view illustrations showing the relationship between the sweep angle and the clocking angle for a representative SMS tool constructed as set forth herein.

FIG. 10 is a flow chart describing a representative method for generating a tool path for a SMS tool.

The present disclosure is susceptible to modifications and alternative forms, with representative embodiments shown by way of example in the drawings and described in detail below. Inventive aspects of this disclosure are not limited to the disclosed embodiments. Rather, the present disclosure is intended to cover alternatives falling within the scope of the disclosure as defined by the appended claims

DETAILED DESCRIPTION

Embodiments of the present disclosure as described herein are intended to serve as examples. Other embodiments can take various and alternative forms. Additionally, the drawings are not necessarily to scale. Some features may be exaggerated or minimized to show details of particular components. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a representative basis for teaching one skilled in the art to variously employ the present disclosure.

Certain terminology may be used in the following description for the purpose of reference only, and thus are not intended to be limiting. For example, terms such as “above” and “below” refer to directions in the drawings to which reference is made. Terms such as “front,” “back,” “fore,” “aft,” “left,” “right,” “rear,” and “side,” describe the orientation and/or location of portions of the components or elements within a consistent but arbitrary frame of reference, which is made clear by reference to the text and the associated drawings describing the components or elements under discussion. Moreover, terms such as “first,” “second,” “third,” and so on may be used to describe separate components. Such terminology may include the words specifically mentioned above, derivatives thereof, and words of similar import.

Referring to the drawings, wherein like reference numbers refer to the same or like components in the several Figures, and beginning with FIG. 1A, a system 10 is shown for use in an Incremental Sheet Forming (ISF) process 100, during which a three-dimensional (3D) part 12 is progressively formed from a planar material blank 11. In a non-limiting exemplary embodiment, the planar material blank 11 may be a thin or thick sheet, e.g., about 0.3 mm to about 5 mm thick, of an application-suitable material such as Aluminum 2024-O or another suitable grade or alloy of aluminum, carbon steel, stainless steel, titanium, etc. Non-metallic or composite materials may be used in other possible embodiments. Solely for illustrative consistency, the planar material blank 11 will be referred to hereinafter as a sheet 11 without limitation, with the sheet 11 having a working surface 110.

The system 10 depicted in FIG. 1A includes a multi-axis drive mechanism 14 connected to a slope-matched stylus (SMS) tool 20. As contemplated herein, the multi-axis drive mechanism 14 may be embodied as a computer numerical control (CNC) machine 14A, e.g., a 3-axis, 4-axis, or 5-axis CNC machine in the several representative embodiments described below. Alternatively, the multi-axis drive mechanism 14 may be a multi-axis serial robot 14B as shown. For instance, the multi-axis serial robot 14B may be embodied as a commercially-available serial robot having sufficient stiffness to control the position of the SMS tool 20, such as a six control degrees of freedom (“6-DoF”), with the multi-axis drive mechanism 14B depicted in FIG. 1A as such a serial robot.

Although omitted from the various Figures for the purpose of illustrative simplicity, the multi-axis drive mechanism 14 includes a CNC control unit 14C configured to execute a toolpath program, e.g., GCODE, when forming the 3D part 12. Exemplary functional configuration and associated programming of the CNC control unit 14C is set forth below with reference to FIG. 10 . Additionally, the multi-axis drive mechanism 14, also referred to generally in the art as a part forming machine, may use a support frame or fixture 25 (see FIGS. 1B, 1C, and 1D) to support some or all of a perimeter of the 3D part 12 and the sheet 11 during forming.

Note that in FIGS. 1B, 1C, and 1D, the sheet 11, the frame 25, and the SMS tool 20 are drawn in the style of a partial cutaway view for the purposes of clarity. Some embodiments may employ a die 46 to support the sheet 11 during forming. Such is the case of two point incremental forming (TPIF), as illustrated in FIG. 1D. In other embodiments, the multi-axis drive mechanism 14 may forego use of the die 46 or other such support, e.g., as in single-point incremental forming (SPIF), using one SMS tool 20. Such a use case is illustrated in FIG. 1B. Likewise, two multi-axis drive mechanisms 14 may be used for dual sided incremental forming (DSIF) using two independently-driven SMS tools 20A and 20B operating in a synchronized fashion, as illustrated in FIG. 1C.

Referring briefly to FIG. 1B, for example, the above-noted SPIF implementation is shown that foregoes use of the die 46 of FIG. 1A. The sheet 11 is secured via the fixture 25 and an applied clamping force (arrows F). The SMS tool 20, having a shaft 22 with longitudinal axis 200, i.e., a center axis, forms a flat line of contact (LL) relative to the working surface 110 of the sheet 11. As appreciated in the art, SPIF may be augmented by forming with the assistance of a planar backing plate (not shown) containing an opening with a shape that matches the perimeter edge of the particular 3D part 12 to be formed.

Additionally, the present teachings may also be extended to DSIF implementations as shown in the partial cutaway view of FIG. 1C. In such an embodiment, separate SMS tools 20A and 20B with respective shafts 22A and 22B having respective longitudinal axes 200A and 200B are used to form opposing working surfaces 110A and 110B of the sheet 11. In this instance, two flat lines of contact LL-A and LL-B exist between the SMS tools 20A and 20B and the respective working surfaces 110A and 110B. Thus, one or more SMS tools 20 may be used within the scope of the disclosure, with or without backing plates, in order to perform a particular variation of the underlying ISF process 100 of FIG. 1A.

An additional exemplary process benefitting from the present teachings is that of two-point incremental forming of FIG. 1D using the die 46, i.e., a male or convex die extending away from a table 19 or other structurally stable and planar surface toward the SMS tool 20 and having a particular surface geometry. In such a use case, the die 46 may be situated on the table 19 underneath the sheet 11, with the sheet 11 clamped in place via clamping forces (arrows F) and the fixture 25 as appreciated in the art. Downward loading forces (arrows L) are also applied to press the sheet 11 firmly up against the die 46. The representative SMS tool 20 is thus usable in a host of different ISF processes, with just a few representative possibilities shown in FIGS. 1A-1D.

Also omitted from FIGS. 1A, 1B, 1C and 1D but well understood in the art, the multi-axis drive mechanism 14 may include a collet or other similar structure configured for securely grasping and holding the SMS tool 20 in a particular orientation, typically but not necessarily the illustrated vertical orientation. Such a collet may be rotatable in certain 4-axis or 5-axis embodiments as set forth below, e.g., by coupling to a spindle that is rotated as needed by operation of a stepper motor, servo motor, or another application-suitable rotary actuator.

Referring again to FIG. 1A, the SMS tool 20 in its various embodiments includes the shaft 22, e.g., a cylindrical rod or elongated shank constructed of an alloy of steel, aluminum, titanium, or another strong, application-suitable material, and a stylus body 24. The shaft 22 has the longitudinal axis 200 and respective first and second distal ends E1 and E2. Thus, the SMS tool 20 connects to the multi-axis drive mechanism 14 as indicated by arrow AA. The first distal end E1 in the illustrated configuration is securely connected to the multi-axis drive mechanism 14, e.g., via the above-noted collet (not shown), while the stylus body 24 is likewise securely connected to or formed integrally with the shaft 22 and disposed at the second distal end E2 thereof.

During the ISF process 100, part or all of a perimeter edge of the sheet 11 is securely clamped by the fixture 25 (see FIGS. 1B, 1C, and 1D) using the applied clamping force (arrows F), e.g., a spring-based, hydraulic, or pneumatic clamp (not shown). Although omitted for clarity, the fixture 25 may be a frame that is movable in a vertical direction, i.e., a z-axis direction in a nominal xyz Cartesian reference frame, with the vertical position controlled via an externally applied force supplied by a bank of pneumatic or hydraulic cylinders (not shown), the working pressure of which is adjustable by a user. Alternatively, the vertical position may be controlled by operation of the multi-axis drive mechanism 14.

Also during the ISF process 100, the stylus body 24 is sequentially pressed into the working surface 110 of the sheet 11 by operation of the multi-axis drive mechanism 14, possibly assisted by the die 46 supported on the table 19. As understood in the art, this action progressively deforms the sheet 11 using step-wise deformations in accordance with a specified constant stepdown distance (Δz) or through a variable stepdown distance which is dependent on the z coordinate (Δz=f(z)). As the present teachings contemplate formation of embodiments of the 3D part 12 having relatively shallow part wall angles (θw), e.g., less than about 20° relative to horizontal in some instances (70° relative to the longitudinal axis 200) or as small as about 5° or less (85° relative to the longitudinal axis 200) in other embodiments, a presented tool wall angle (θ_(T)) of the stylus body 24 is configured to complement/match the part wall angle(s) (θ_(w)) of the 3D part 12 via the structural configuration options described below. That is,

${\theta_{w} + \theta_{T}} = {\frac{\pi}{2}.}$

A corresponding method 50 for forming the 3D part 12 is likewise described below with reference to FIG. 8 , with a method 80 for generating a tool path described below with reference to FIG. 10 .

Referring now to FIG. 2A, the particular geometry defining the body of the exemplary SMS tool 20 of FIGS. 1A-1D can be described as the frustum of a cone 71. As defined here, the term ‘cone’ refers to a general form of a cone having an arbitrary cross section, and which may be slanted as depicted in FIGS. 2A and 2B. The cone 71 is defined by an origin point O positioned at the apex 72 of the cone 71, as well as a cross section contained within a top tool plane 73, with the top tool plane 73 being positioned a distance (h) above an apex plane 74 which contains the origin point O. A bottom tool plane 75 defines the depth of the SMS tool 20 described herein, with the bottom tool plane 75 located a distance (d) away from the apex plane 74.

Any line 701 which connects a point 900 on the cross section curve to the origin point O, i.e., the apex 72 of the cone 71, is a line of constant tool wall angle (θ_(T)) . All of these possible lines 701 taken together form the tool surface, generally represented in FIG. 3 and FIGS. 5A-D as tool surface 26 and forming the working surface of the stylus body 24, i.e., the particular presented surface of the SMS tool 20 that interfaces directly with the working surface 110 of the sheet 11 as depicted in simplified form in FIG. 1A. As such, the tool surface 26 defines a range of tool wall angles (θ_(T)). As noted above, the tool wall angle (θ_(T)) shown schematically in FIG. 1A geometrically complements a part wall angle (θ_(W)) of the 3D part 12, with a flat line of contact (LL) provided between the tool surface 26 and the sheet 11 during the ISF process 100 of FIG. 1A, with such a line of contact depicted in a simplified schematic diagram in FIGS. 1A-1D.

Still referring to FIG. 2A, the cross section on the top tool plane 73 can be described by some function of the sweep angle (α). As an example, the distance (s) from the point 90 in the top tool plane 73 to a given point 900 on the cross section can be described by some function s(α), where the angular value of (α) lies in the range [−π,π). That is, in understood set theory notation, [A,B] is the range A to B, including A and B, whereas [A,B) is the range A to B but excluding B. The range [−π,π) thus ensures that there is no resulting point of overlap. Alternatively, the tool wall angle (θ_(T)) can be expressed as a function of the of sweep angle (α), i.e., θ_(T)=θ_(T)(α). These forms are equivalent and can be converted through simple trigonometry, as illustrated in FIG. 2C and discussed below.

It is understood that, because the described surface is conical, the cross section on the bottom tool plane 75 of FIGS. 2A and 2B is completely driven by the cross section on the upper tool plane 73 togther with the position of the origin point O and the distances (d) and (h). Therefore, the function s(α) together with the position of the origin point O and the values of distances (h) and (d) fully defines the stylus body 24 of the SMS tool 20.

Referring now to FIG. 2B, the shaft 22 meets the top tool plane 73 of the stylus body 24 (e.g., FIG. 1A) at some attachment point 95. Specifically, attachment point 95 is the point of intersection of the longitudinal axis 200 of shaft 22 and the top tool plane 73. Optionally, this attachment point 95 may be located on a line 700 extending between the origin point O and point 90, in which case the shaft 22 sits directly above the origin point O (i.e., the apex 72 of the cone 71) and the line 700 is coincident with longitudinal axis 200. This is the case with the representative embodiment shown in FIG. 3 .

In other cases there may be some offset. For example, the representative embodiments shown in FIGS. 4A-E contain a non-zero value for the offset distance (k) as shown in FIG. 2B and a zero value for the offset distance (g). In comparison, the embodiment shown in FIGS. 5A-D have a non-zero value for the offset distance (k) as well as a non-zero value for the offset distance (g). In general, it is understood that such offsets will be driven by design considerations such as structural integrity and functionality of the SMS tool 20. It is also understood that the diameter and height of the shaft 22, and various fillet radii, are also required dimensions to fully specify the SMS tool 20 geometry, but as these do not alter the functionality of the tool they are omitted for clarity.

In the representative view of FIG. 2C, the distance (h) between the top tool plane 73 and the apex plane 74 (FIGS. 2A and 2B) is shown with the distance (s) from point 90 to point 900 of FIG. 2A. The distance (s) may be a function s(α) in some embodiments, i.e., in non axisymmetric embodiments. In such embodiments the tool wall angle (θ_(T)) is likewise a function of (α), i.e.,:

${\theta_{T}(\alpha)} = {\tan^{- 1}\left( \frac{s(\alpha)}{h} \right)}$

where h≠0.

In FIG. 3 , the simplest embodiment of the SMS 20 tool of FIG. 1A is shown. Here, the cone 71 previously referred to in FIGS. 2A and 2B takes the form of an exemplary right angled circular cone. In this embodiment, the flat line of contact (LL) shown schematically in FIG. 1B, FIG. 1C (LL-A and LL-B), and 1D is provided by a conical, rounded-nose stylus body 240 that includes a planar base surface 30, located within the top tool plane 73 of FIGS. 2A and 2B, with the planar base surface 30 having a circular perimeter surface 29. The planar base surface 30 is connected to the shaft 22 and arranged orthogonal to the longitudinal axis 200. Being conical in shape, the tool surface 26 extends as angled side walls 260 from the base surface 30 and tapers at the tool wall angle (θ_(T)) noted above, with the angled side walls 260 terminating at a radiused or rounded tip 21 of the stylus body 240.

For example, when the stylus body 240 is axisymmetrical with respect to the longitudinal axis 200, the stylus body 240 defines a single tool angle, which in turn corresponds to a cone half angle (CHA) of the defined conical shape. As appreciated, the term “CHA” describes the extent to which an incident beam converges or diverges respectively on or away from a point, in this instance a point at an apex of the rounded tip 21. The single tool wall angle (θ_(T)) in a possible embodiment may be less than about 20°, down to about 5° or possibly less, e.g., 2-3°. Motion control of the SMS tool 20 in this simplified embodiment may be performed via the exemplary multi-axis drive mechanism 14 of FIG. 1A when the multi-axis drive mechanism 14 is configured as 3-axis CNC machine. That is, as just one tool wall angle (θ_(T)) is provided by a given SMS tool 20 in the non-limiting right angled conical configuration, drive control is required for translation of the tool in the x, y, and z-axes only.

Unlike conventional hemispherical or bull-nosed stylus tools, which contact a sheet in a very small region, the flat line of contact (LL) enabled by the stylus body 240 of FIG. 3 ensures that a wider zone of material is elastoplastically deformed at any given point in time during the ISF process 100 of FIG. 1A. Using a CHA that is complementary to the part wall angle (θ_(W)) for a 3D part 12 having a constant, shallow part wall angle (θ_(W)) thus has the desirable effect of minimizing springback, curl/surface waviness, and wasteful scrap. This in turn may enable a larger stepdown distance (Δz of FIG. 1A) to be used, thereby reducing cycle time as an additional benefit.

Forming multi-angled 3D parts 12 remains possible with a single tool wall angle configuration. However, doing so would require frequent replacement of a given SMS tool 20 with an appropriate slope-matched variant, as will be appreciated by those skilled in the art. To that end, and referring now to FIGS. 4A-4E, the SMS tool 20 described above may be provided with an alternative stylus body 340 with angled side walls 260 forming a defined sweep range inclusive of multiple corresponding tool wall angles. Such a configuration would avoid the need for replacing single-angle tools of the type described above every time a tool wall angle changes along a given toolpath contour. For clarity, the stylus body 340 is variously depicted in cross section view (FIG. 4A), plan view (FIGS. 4B and 4C), and respective bottom and top perspective views (FIGS. 4D and 4E), with the illustrated shape and contour being just one possible implemention of the stylus body 340.

Referring again briefly to FIG. 2B, this particular embodiment relates to a conical surface which is a slanted cone with a general convex cross section that is symmetric about about the line α=0. Here the function s(α) is smooth and even, such that s(α)=s(−α), and the function defines a convex cross section on the top tool plane 73. In the configuration shown there exists a non-zero offset distance (k) and the offset distance (g) between parallel lines 500 and 501 respectively intersecting points 90 and 95 is equal to zero, with lines 500 and 501 being perpendicular to lines 600 and 601 such that (k) and (g) are offsets in different axes, e.g., nominal x and y axes of a Cartesian reference frame. Other offset values are possible which correspond to a different attachment points of the shaft 22.

Relative to the conical/single tool angle configuration of FIG. 3 , and with resumed reference to FIG. 4A, the stylus body 340 includes the angled side wall 260 providing a working surface that itself definines a range of tool angles, the latter in turn defining the sweep angle range. To select the flat line of contact (LL) at any given moment during the ISF process 100 of FIG. 1A, the drive mechanism 14 rotates the SMS tool 20 about the longitudinal axis 200, causing rotation of the stylus body 340 relative to the 3D part 12 being formed. Continuous contour variation between the relatively shallow wall angle and the relatively steep wall angle enables formation of the 3D part 12 with varying slopes or part wall angles (θ_(W)) without having to change the SMS tool 20 during the ISF process 100.

As already described, in the most general form the walls of the stylus body 340 form a conical frustum. The term ‘frustum’ refers to a shape which is defined between two parallel planes, and it is understood that the term ‘cone’ refers to surface with an apex point and some cross section which converges towards the apex point. The cross section may be a circular cross section such as in the case of the non-limiting representative embodiment shown in FIG. 3 . Alternatively, the cross section may be a shape which contains only one line of symmetry, as is the case of the embodiment shown in FIGS. 4A-4E. In the most general case of an SMS tool 20, such as the embodiment shown in FIGS. 5A-5D, the cross section may be an arbitrary convex shape with no symmetry present.

Still referring to FIG. 4A, the cross section is defined by the plane which passes through both the longitudinal axis 200 and the line 700 noted above and depicted in FIGS. 2A and 2B. Imaginary lines L₁ and L₂ define relevant tool wall angles θ_(A) and θ_(B), and intersect in free space at origin point O, which is the apex 72 of the aforementioned general cone 71 shown in FIGS. 2A and 2B. Line 700 is defined parallel to longitudinal axis 200 and passes through the origin point O. In some but not all embodiments, the angle θ_(A) is the maximum angle θ_(max) in the sweep angle range, and the angle θ_(B) is the minimum angle θ_(min). In general, it is understood that this arrangement will depend on the position of attachment of the shaft 22 onto the planar base surface 30, which may be chosen arbitrarily.

The corresponding tool angles in FIG. 4A may include the relatively shallow tool wall angle (θ_(B)) in a non-limiting exemplary range of about 5° to about 20°, and a relatively steep tool wall angle (θ_(A)) in an exemplary range of about 55° to about 70° or even as much as about 90°, such that “shallow” and “steep” are relative terms. In another exemplary configuration, the shallow tool wall angle (θ_(B)) is about 10° and the steep tool wall angle (θ_(A)) is about 60°, with other possible sweep ranges usable in other embodiments. The stylus tool 20 and the stylus head 340 are configured to form the 3D part 12 with part wall angles (θ_(W)) that vary within such a defined sweep range, i.e., from θ_(A) to θ_(B), and anywhere in between. Incremental angular variation may be achieved in real-time via a 4-axis CNC machine embodiment of the drive mechanism 14, or by another 4⁺-axis robot, with sufficient stiffness to maintain the required stylus position, such that the presented tool angle matches the required tool wall angle for forming a given part wall angle.

The contoured/swept features of the stylus body 340 in the representative embodiment of FIG. 4A can be further visualized with reference to FIGS. 4B, 4D, and 4E, with the shaft 22 extending toward the multi-axis drive mechanism 14. The stylus body 340 in this particular configuration has a generally ovate perimeter in plan view (FIG. 4B), i.e., having rounded toe region 31 that flares outward in an arcuate manner toward an oppositely disposed rounded heel region 33, relative to a longitudinal axis 200 of the shaft 22. The upper surface 30 of the stylus body 340, which is a non-working surface, gently slopes away from the shaft 22 to a perimeter edge 32 of the stylus body 340. Thus, from the cross section view of FIG. 4A and perspective view of FIG. 4E, the upper surface 30 presents a relatively low profile, with the swept working surfaces of the stylus body 340 and most of the mass thereof located on an underside of the SMS tool 20 as best shown in FIG. 4E.

As shown in FIG. 4D, the underside of the SMS tool 20 defines the contoured tool surfaces 360 of the stylus body 340, which are the working surfaces of the stylus body 340 defining the above-described sweep angle range. The tool surfaces 360 vary non-linearly as one transitions from a point on the toe region 31 to a point on the heel region 33, with the toe-to-heel sweep corresponding to the shallow tool wall angle (θ_(B)) (see FIG. 4A). The aforementioned steep tool wall angle (θ_(A) of FIG. 4A) is defined by the sweep of the stylus body 340 at a location diameterically opposite the toe region 31. Rotation of the stylus tool 20 about the longitudinal axis 200 thus presents the tool wall angle required to complement the part wall angle, such that the flat line of contact (LL of FIGS. 1B-1E) is formed between the stylus body 340 and the sheet 11 during the ISF process 100.

Referring briefly again to FIG. 2A and FIG. 4C, it is useful to define two further angles, both of which lie within the top tool plane 73. The first angle is the sweep angle (α), which is the angle subtended between line 500 and the line of length (s) which runs between the points 90 and 900. The second is the clocking angle (ω), which is the angle subtended between line 500 and the line which runs between the points 95 (see FIG. 2B) and 900. It is understood that, in general, these angles will differ for arbitrary points 900 on the cross section, except in the case of zero offset distances (g) and (k).

In FIG. 2A, a line 701 of constant tool wall angle (θ_(T)) is present between the origin point O (apex 72) and any point 900 on the cross section defined in the top tool plane 73. If an SMS tool 20 contains a range of tool wall angles, this wall angle may change with respect to the sweep angle (α). In such a case, during forming, an SMS tool 20 has a first sweep angle α₁ which corresponds to some first tool wall angle θ_(T1), complementing the current part wall angle. After some period of time, the SMS tool 20 may encounter a change in the wall angle of the 3D part 12. If SMS tool 20 has a range of tool wall angles, it can rotate through some range of sweep angles Δα in order to reach a second sweep angle α₂, which corresponds to some second tool wall angle θ_(T2), complementing the new part wall angle.

Referring now to FIGS. 2B, 9A, and 9B, rotation of the SMS tool 20 is facilitated by CNC control unit 14C of FIG. 1A only through its connection with the shaft 22. In FIGS. 9A and 9B, the attachment point 95 after rotation about point 90 is represented as attachment point 95′, with the new location of the shaft 22 shown as 22′. It is understood that a rotation Δα about the origin point O cannot be reproduced through a rotation Δω about the attachment point 95 alone. To achieve the same tool position and orientation, the SMS tool 20 must first undergo a (clocking) rotation, Δω, followed by, or combined with, a translation of the SMS tool 20. The only instance in which a translation is not required is the case of offset distances (g) and (k) being equal to zero.

As shown in FIGS. 2A and 2C, the cross section generated by some s(α) will not, in general, provide a linear relationship between the sweep angle (α) and the tool wall angle (θ_(T)). As a result, the rate of change of the tool wall angle with respect to the sweep angle (α) may differ for different values of sweep angle (α). In practice, therefore, at one end of the stylus body 340, the sweep angle (α), and hence also the clocking angle (ω), must rotate through a large angular distance in order to produce relatively small change in the tool angle (θ_(T)). At the other end of the stylus body 340 only a small change in the sweep angle (α), and hence also the clocking angle (ω), will produce a relatively large change in the tool wall angle (θ_(T)). Such geometry is thus accounted for in toolpath planning as described below with reference to FIG. 10 .

Referring now to FIG. 6 , in some embodiments the multi-axis drive mechanism 14 of FIG. 1A may be configured as a 5-axis CNC machine or other device capable of 5-axis motion. Addition of the 5th axis, while adding to control complexity, has the benefit of simplifying the configuration of the stylus tool 20 in some respects. For example, an alternative construction of the SMS tool 20 may include a stylus body 440 disposed at the second distal end E2 of the shaft 22. The stylus body 440 defines a flat/planar bottom tool surface 42 arranged normal to the longitudinal axis 200 of the shaft 22. The sheet 11 of FIGS. 1A, 1B, and 1C, omitted from FIG. 6 for clarity, would be located between the planar bottom tool surface 42 of the stylus body 440 and a representative fixture 46, as appreciated in the art.

As illustrated, multi-axis drive mechanism 14 of FIG. 1A, when embodied with requisite 5-axis capabilities, controls the orientation or attitude of the SMS tool 20 with the stylus body 440 of FIG. 6 . In particular, the multi-axis drive mechanims 14 ensures that the planar bottom tool surface 42 of the stylus body 440 remains properly aligned to the local tangent plane 47, i.e., the longitudinal axis 200 of the shaft 22 remains colinear with the surface normal at points in contact with the SMS tool 20.

As will be appreciated by those skilled in the art, the present teachings lend themselves to ISF methodologies that, when performed with the new class of SMS tool 20 of FIGS. 1A-6 , greatly reduces springback and surface waviness often experienced during ISF processes performed using standard hemispherical stylus tools.

As an example, and with reference to the TPIF process illustrated in FIG. 1D, FIG. 7 depicts representative sheet 11 formed into a shallow-walled part 12S using the SMS tool 20, with the representative tootpath depicted as lines 99. The representative part 12S has a constant shallow part wall angle of, e.g., 5°. Were such a 3D part 12S to be manufactured using, e.g., a 30 mm diameter hemispherical stylus tool having a constant stepdown ΔZ of 5 mm, the resulting sheet 111 shown for comparison would have a high level of surface waviness 111W. In contrast the present solutions achieved using the SMS tool 20 as described in detail herein allow the same step down to be used, if desired, possibly using a constant tool angle that complements the constant part wall angle of 5°. As a result, significantly lower levels of surface waviness 11W are imparted to the final 3D part 12 by the SMS tool 20, as illustrated in FIG. 7 . The SMS tool 20 thus helps overcome the problematic issue of surface waviness by ensuring the line of contact (LL) with the sheet 11. The line of contact (LL) also grealty reduces the residual stress in the formed 3D part 12. As a result, there is much less springback.

An example method 50 providing such benefits is shown in FIG. 8 , and commences at block B52 with securing part or all of a perimeter edge of the sheet 11 to the fixture 25. Such an action may entail securing the sheet 11 to a moveable frame via clamps and a suitable clamping force (arrows F of FIGS. 1A, 1B,1C and 1D) as noted above.

The method 50 proceeds to block B54 once the sheet 11 has been secured in preparation for ISF deformation, which includes connecting the first distal end E1 of the shaft 22 of the SMS tool 20, in any of its disclosed embodiments, to a suitably configured version of the multi-axis drive mechanism 14, e.g., a 3-axis, 4-axis, or 5-axis CNC machine or robot.

Once blocks B52 and B54 are complete in either possible order, the method 50 proceeds to block B56. There, the multi-axis drive mechanism 14 of FIG. 1A progressively presses a tool surface 26 of the SMS tool 20 into or against the sheet 11 to form the 3D part 12. As explained above, the tool surface 26 has at least one corresponding tool wall angle (θ_(T)) relative to a longitudinal axis 200 of the shaft 22 that complements a part wall angle (θ_(W)) of the 3D part 12, such that the flat line of contact (LL) is provided between the stylus body 24, 240, 340, 440 or 540 and the sheet 11 during the ISF process 100.

In a possible implementation, the corresponding tool wall angle (θ_(T)) may be single tool angle of less than about 20°, in which case progressively pressing the tool surface 26 of the stylus body 240 or its alternative embodiments into or against the sheet 11 may include using a 3-axis CNC machine as the multi-axis drive mechanism 14 to control translation of the SMS tool 20 in three dimensions. In other embodiments when the 3D part 12 has multiple part wall angles, and when the corresponding tool tool angle (θ_(T)) of the stylus body 340 or 540 includes multiple corresponding tool wall angles (θ_(T)) together defining an angular sweep range, progressively pressing the tool surface 26 into or against the sheet 11 may include using a 4-axis drive mechanism as the multi-axis drive mechanism 14 to control the translation and rotation about longitudinal axis 200 of the SMS tool 20.

Alternatively, when the at least one tool surface of the stylus body 440 of FIG. 6 is a planar bottom tool surface 42 arranged orthogonally with respect to the longitudinal axis 200 of the shaft 22, the multi-axis drive mechanism 14 may be a 5-axis drive mechanism, and the pressing the tool surface 42 of the stylus body 440 into or against the sheet 11 includes maintaining alignment of tool surface 42 with the local tangent plane 47 of the 3D part 12 during the ISF process 100 via the 5-axis drive mechanism. In at least one embodiment, this includes using the 5-axis drive mechanism as the multi-axis drive mechanism 14 to control the translation of the SMS tool 20 in three dimensions, as well as the rotation about the longitudinal axis 200 and the rotation about a further axis (not shown) which is orthogonal to the longitudinal axis 200.

TOOLPATH GENERATION: As appreciated in the art of ISF, in order to perform an ISF process on the CNC machine 14A shown in FIG. 1A, one must first construct a toolpath that is to be followed by the SMS tool 20 in the course of forming the 3D part 12.

Referring to FIG. 10 , an exemplary method 80 is shown that describes, in simplified form, a process for creating a useable toolpath for an SMS tool 20 constructed as set forth herein. The created toolpath is then executed as code or instructions by the CNC control unit 14C, e.g., of the exemplary CNC machine 14A of FIG. 1A.

Beginning with block B81 a part geometry is input into a toolpath generation program, e.g., by uploading a corresponding CAD file for block B81. Such a CAD file may describe a set of trimmed parametric surface entities and their related entities such as edges and vertices, as with STEP, Parasolids, ACIS, or IGES files. Alternatively, the file may describe a set of vertices and connecting polygons such as is the case with STL, PLY, VRML files or the like. Furthermore, the CAD data in block B81 may be in the form of a native file format to CAD software such as 3DEXPERIENCE, CATIA, SOLIDWORKS, CREO, SOLIDEDGE, Siemens® NX, or the like.

In block B82, and with reference to FIGS. 2A and 2B, an SMS tool 20 is defined by providing values (h), (d), (k), (g) and some function which relates the distance between point 90 and some cross section point 900, denoted as distance (s), with the sweep angle (α), where (α) is defined in the range [−π, π) as noted above. The method 80 then proceeds to block B83.

At block B83, the method 80 includes determining a sheet offset surface. This may involve offsetting the part geometry by a prescribed distance, typically but not necessarily the sheet thickness, with the intention of avoiding marring or gouging of the 3D part 12. Block B83 may be eliminated if one can assume this variable is properly accounted for in block B81. If the sheet offset surface is not in the form of a set of vertices and connecting polygons at this step then it is discretised to convert the surface into this format. The method 80 then proceeds to block B84.

At block B84, a first vertex is selected from the set vertices that describe the (discretized) sheet offset surface. The method 80 then proceeds to block B85 where the outwards pointing unit normal vector ({circumflex over (n)}) at the current vertex of the sheet offset surface is computed.

At block B86 of FIG. 10 , the program for toolpath generation next computes the local surface part wall angle of the 3D part 12 at the selected vertex, i.e., θ_(w)=cos⁻¹(1_(z)·{circumflex over (n)}), where 1 _(z) represents a unit vector parallel to the longitudinal axis 200. At subsequent block B88, a corresponding sweep angle (α) is found which provides the tool wall angle (θ_(T)) that complements a part wall angle θ_(w).

Referring to FIGS. 2A and 2C, each tool wall angle (θ_(T)) corresponds to one or more values of the sweep angle (α) and the related distance s(α). Given this relationship, the sweep angle (α) of the SMS tool 20 can be determined for any given tool angle (θ_(T)). In some embodiments of SMS tool 20, more than one value of α corresponds to a given tool wall angle (θ_(T)) due to symmetry in the tool cross section. This is the case in FIGS. 4A-4E. In such cases, it is understood that any value of the sweep angle (α) that corresponds to the required tool wall angle (θ_(T)) may be selected upon first contact of the SMS tool 20 with the sheet 11. However, as forming progresses, if more than one sweep angle provides the required tool wall angle (θ_(T)) then the current sweep angle (α) can be selected based on the proximity to the sweep angle at the previous step in the toolpath.

Given the sweep angle (α), the program can readily locate the proper contact point on the SMS tool 20 with respect to x_(tool), or point 70 of FIG. 4A when referencing off of the longitudinal axis 200. This calculation is performed at block B89. Note that the contact point lies on a plane spanned by 1_(z), and the line of contact (LL) defined or established by the sweep angle (α). This depends on where the SMS tool 20 makes its contact, which in turn may be as close to the base of the SMS tool 20 as possible to avoid gouging.

Still referring to FIG. 10 , at block B90 the toolpath generation program determines the required translation and clocking angle rotation (Δω), i.e., the required rotation for the SMS tool 20 about longitudinal axis 200, such that the contact point on SMS tool 20 coincides with the selected vertex on the (discretized) sheet offset surface, and the horizontal component of the normal of the SMS tool 20, at the point of contact point, is vectorially opposite to the horizontal component of the surface normal {circumflex over (n)}.

Once this is accomplished, the method 80 proceeds to block B91 where the toolpath generation program stores the new position of x_(tool) as well as the required clocking angle rotation of the tool, in accessible memory. If at subsequent block B92 it is determined that all vertices within the set of vertices which describe the discretized surface have been processed, the method 80 proceeds to block B93. If this criteria has not been met the method 80 will instead return to block B84.

At block B93, with all points processed, the calculated tool positions define the full tool offset surface. From there, the method 80 finishes at block B94 by generating the toolpath from the tool offset surface via the toolpath generation program. Typically this may be through taking z-level slices of the tool offset surface to generate contours however other toolpath generation methods may also be used. Contours in other planes may also be used in order to generate subsequent ‘lace’ toolpaths which traverse the part in a zig-zag fashion. Such toolpath may be used following a z-level toolpath. Rotations of the SMS tool 20 are given at each point from the value stored with each tool offset surface point.

Finally, once all toolpaths have been generated in the above summarized manner, the toolpath information is transferred to the CNC control unit 14C, which processes the generated toolpath information in order to command translation and/or rotation of the SMS tool 20 to the sequence of instructed positions. This transfer may involve toolpath data in the form of ASCII or binary data files. For example, the transfer may involve saving the toolpath data from within the toolpath generation program, in an ASCII text format such as GCODE, and subsequently loading the file into the CNC control unit 14C, which in turns drives the CNC machine 14A when forming the 3D part 12.

The present solutions extend the benefits of ISF processes to the manufacturing of 3D parts 12 having one or more shallow part wall angles. For instance, aircraft and other complex systems having long lifecycles often rely on availability of parts long after the system is out of production. To that end, the required parts could be rapidly produced using the disclosed ISF method 50 and the various SMS tools 20, either with axisymmetric features or non-axisymmetric features. With respect to at least some of the attendant benefits of the foregoing disclosure, the foregoing disclosure enables production of 3D parts 12 with reduced springback and surface waviness relative to production of 3D parts 12 with very shallow part wall angles and mild curvatures using conventional hemispherical stylus tooling. These and other benefits will be readily appreciated by those skilled in the art in view of the foregoing disclosure.While some of the best modes and other embodiments have been described in detail, various alternative designs and embodiments exist for practicing the present teachings defined in the appended claims. Those skilled in the art will recognize that modifications may be made to the disclosed embodiments without departing from the scope of the present disclosure. Moreover, the present concepts expressly include combinations and sub-combinations of the described elements and features. The detailed description and the drawings are supportive and descriptive of the present teachings, with the scope of the present teachings defined solely by the claims. 

What is claimed is:
 1. A slope-matched stylus (SMS) tool for an Incremental Sheet Forming (ISF) process in which a three-dimensional (3D) part is progressively fabricated from a sheet, the SMS tool comprising: a shaft having a longitudinal axis, a first distal end, and a second distal end, wherein the first distal end of the shaft is configured to connect to a multi-axis drive mechanism; and a stylus body connected to the second distal end of the shaft, wherein the stylus body has at least one tool surface defining, relative to the longitudinal axis of the shaft, a corresponding tool wall angle that matches a part wall angle of the 3D part such that the corresponding tool wall angle and the part wall angle form complemementary angles, and wherein a flat line of contact is present between the stylus body and a working surface of the sheet during the ISF process.
 2. The SMS tool of claim 1, wherein the stylus body is conical, and includes a base surface connected to the second distal end of the shaft, and a side wall extending axially from the base surface toward a rounded tip of the stylus body, and wherein the at least one tool surface defines the corresponding tool wall angle.
 3. The SMS tool of claim 2, wherein the corresponding tool wall angle includes a single tool wall angle of less than about 20°.
 4. The SMS tool of claim 1, wherein a non-linear relationship exists between the corresponding tool wall angle and a sweep angle of the SMS tool.
 5. The SMS tool of claim 1, wherein the corresponding tool wall angle includes a relatively shallow tool wall angle in a range of about 5° to about 20°, and a relatively steep tool wall angle in a range of about 55° to about 70°, such that the stylus body is configured to form the 3D part with a part wall angle varying anywhere within a range of about 5° to about 70°.
 6. The SMS tool of claim 5, wherein the relatively shallow tool wall angle is about 10° and the relatively steep tool wall angle is about 60°.
 7. The SMS tool of claim 1, wherein the at least one tool surface is a planar tool surface arranged orthogonal to the longitudinal axis of the shaft, the multi-axis drive mechanism is a 5-axis drive mechanism, and the longditudinal axis of the shaft is aligned normal to the working surface of the 3D part at the line or plane of contact by operation of the 5-axis drive mechanism.
 8. A system for use in an Incremental Sheet Forming (ISF) process during which a three-dimensional (3D) part is progressively fabricated from a sheet, the system comprising: a multi-axis drive mechanism; and a slope-matched stylus (SMS) tool, including: a shaft having a longitudinal axis, a first distal end connected to the multi-axis drive mechanism, and a second distal end; and a stylus body connected to the second distal end of the shaft, wherein the stylus body includes at least one tool surface defining, relative to the longitudinal axis of the shaft, a corresponding tool wall angle that matches a part wall angle of the 3D part such that the corresponding tool wall angle and the part wall angle form complemementary angles, and wherein a flat line of contact is provided between the stylus body and a working surface of the sheet during the ISF process.
 9. The system of claim 8, wherein the stylus body is conical and includes a base surface connected to the second distal end of the shaft, and a side wall extending axially from the base surface toward a rounded tip of the stylus body, and wherein the at least one tool surface defines the corresponding tool wall angle.
 10. The system of claim 9, wherein the corresponding tool wall angle includes a single slope of less than about 20°.
 11. The system of claim 9, wherein the 3D part defines multiple different part wall angles, the corresponding tool wall angle includes multiple corresponding tool wall angles defining a sweep angle range, and the multiple corresponding tool wall angles form a subset of the sweep angle range, and wherein the multi-axis drive mechanism is a 4-axis drive mechanism.
 12. The system of claim 11, wherein the sweep angle range has a minimum tool wall angle in a range of about 5° to 20°, and a maximum tool wall angle in a range of about 55° to 70°.
 13. The system of claim 12, wherein the minimum tool wall angle is about 10° and the maximum tool wall angle is about 60°.
 14. The system of claim 8, wherein the multi-axis drive mechanism includes a CNC machine.
 15. The system of claim 8, wherein the at least one tool surface is a planar tool surface arranged orthogonal to the longitudinal axis of the shaft, the multi-axis drive mechanism is a 5-axis drive mechanism, and the longitudinal axis of the shaft is aligned approximately normal to the working surface of the 3D part at the line or plane of contact by the 5-axis drive mechanism during the ISF process.
 16. An Incremental Sheet Forming (ISF) method during which a three-dimensional (3D) part is progressively fabricated from a sheet, comprising: securing the sheet to a fixture; connecting a first distal end of a shaft of a slope-matched stylus (SMS) tool to a multi-axis drive mechanism, the SMS tool having a stylus body connected to a second distal end of the shaft, wherein a tool surface of the SMS tool has a corresponding tool wall angle of less than about 20° that matches a part wall angle of the 3D part such that the corresponding tool wall angle and the part wall angle form complemementary angles, and such that a flat line of contact is provided between the stylus body and the sheet; and progressively pressing a tool surface of the stylus body into or against the sheet using the multi-axis drive mechanism to thereby form the 3D part.
 17. The method of claim 16, wherein the corresponding tool wall angle is a single tool wall angle of less than about 20°, and progressively pressing the working surface of the stylus body into or against the sheet includes using a 3-axis CNC machine as the multi-axis drive mechanism to control translation of the SMS tool in a three-dimensional space.
 18. The method of claim 16, wherein the 3D part has multiple different part wall angles, the stylus body defines a sweep angle range inclusive of multiple corresponding tool wall angles, and progressively pressing the working surface of the stylus body into or against the sheet includes using a 4-axis drive mechanism as the multi-axis drive mechanism to control translation of the SMS tool in the three-dimensional space and rotation of the SMS tool about a longitudinal axis of the shaft, to match the tool wall angle to one of the multiple different part wall angles.
 19. The method of claim 16, wherein the working surface of the stylus body is arranged orthogonally with respect to the longitudinal axis of the shaft, the multi-axis drive mechanism is a 5-axis drive mechanism, and the pressing the working surface of the stylus body into or against the sheet includes using a 5-axis drive mechanism to align the longitudinal axis of the tool shaft approximately normal to the surface of the 3D part along the flat line or plane of contact to maintain alignment of the planar bottom tool surface with a local tangent plane of the 3D part.
 20. The ISF method of claim 16, wherein the SMS tool has a sweep range having a shallow tool wall angle in the range of about 5-25 degrees and a steep tool wall angle in the range of about 70-90 degrees, and progressively pressing the tool surface of the stylus body into or against the sheet includes progressively pressing the tool into or against the sheet. 